Hi perado,
apparently you were onto something because now equation 5.7 in that thesis has a different result - try downloading a new copy of it.
In any case once you have a rational function in the form
Y(s)= Y0 (1+s/z1)(1+s/z2)/(1+s/p1)
Y0 = gm1 gm2 / gds1
z1 ~ gm2/Cgs2
z2 ~ gm1/Cgd2
p1 = gds1/Cgs2
under the assumption of saturation and gm1~gm2 then you can always shift your approximation to different frequency ranges
Notice that
p1<<z1<<z2
So let's say you are trying to look at the frequency behavior around z1 then
1+s/p1 ~ s/p1
1+s/z2 ~ 1
and you are left with
Y ~ Y0 p1 (1+s/z1)/s = Y0 p1 / s + Y0 p1 / z1 = 1/(s Leq) + Geq
where you can easily identify an inductive term and a resistive term (in parallel)
Leq = 1/(Y0 p1) = Cgs2 / gm1 gm2
Geq = Y0 p1 /z1 ~ gm1
Now what he is trying to do is to model this over a wider (possibly the entire) frequency range... you have two options: you assume his equivalent circuit is correct and calculate its Y and compare it to the one above OR more skeptically (one would not be surprised this new result is messed up as well) you expand the expression above to get something in the form
Y(s)= B (z1+s)(z2+s)/(p1+s) = B (z1-p1+(p1+s))(z2+s)/(p1+s)= B [ (z2+s) + (z1-p1)(z2+s)/(p1+s) ] =
= B [ (z2+s) + (z1-p1)(z2-p1+(p1+s))/(p1+s) ] = B [ (z2+s) + (z1-p1) + (z1-p1)(z2-p1)/(p1+s)]
where [assuming I did not make a mistake] you can easily identify a parallel combination of admittances
-) Ceq = B = Y0 p1 / (z1 z2) ~ Cgd2
-) Geq = B(z1+z2-p1) ~ B z2 ~ gm1
-) a third term
~ B z1 z2 / (p1 + s)
which can be written as the admittance of the series of one Req and one Leq : 1/R 1/sL / (1/sL +1/R) = 1/L / (s + R/L)
Leq = 1 / (B z1 z2) = 1 / (Y0 p1) = Cgs2 / gm1 gm2
Req = p1 / (B z1 z2) = 1/ Y0 = gds1/gm1 gm2
In summary the new expression 5.7 is still wrong
Of course I am assuming the initial form was correct (which I very much doubt now) and that I did not make a mistake in my calculation (very much possible)
I will double check later, you should do the same
---------- Post added at 12:01 ---------- Previous post was at 10:45 ----------
It looks like our author (or myself - since I have not rechecked my math) was caught in a moment of mathematical weakness; I am getting from his circuit
Y(s) = s Cgs1 + (gm2 + s Cgs2) / (gds1 + s Cgs2)
which gives the same
Leq, Req, Geq
but
Ceq = Cgs1
which makes a lot more sense
____________
There is an error in this last expression for Y(s) see next post for the correct result